Question

# Anomalies in the spectrum of hydrogen atoms

The hydrogen spectral lines are organized in various series. Lyman series are the lines corresponding to transitions targeting the ground state.

Most pictures dealing with hydrogen spectra and available in the web are recordings dealing with extraterrestrial hydrogen sitting in celestial entities. Otherwise they are illustrations obtained not from experimental recordings, but from the well known Rydberg formula.

Of interest for the undersigned are pictures of Lyman series as recorded in laboratory observations of hydrogen atoms, with the atoms sitting in the laboratory itself. Not extraterrestrial hydrogen, nor molecules H2, even if the molecules are sitting nearby.

Presumably such recordings would have required ultraviolet sensitive CCDs, UV photographic plates, or similars. Particularly relevant would be careful raw recordings of Lyman series that INCLUDE THE ALPHA-LINE at 1216 Å.

Experimental remarks about the Lyman alpha-line, difficulties to observe it ---if any---, line width, line broadening, etc., and difficult-to-explain anomalies, are of particular concern. So far Web searching has not been successful.

I would appreciate any link or suggestions as to how to obtain the pictures and experimentally based information of the kind explained above.

Most cordially,
Daniel Crespin

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• Daniel Crespin · Central University of Venezuela
Hello everybody.

The above questions have the following motivation.

In 1914 Theodore Lyman published "The Spectroscopy of the Extreme Ultraviolet", a delicious description of his many years of scientific work dedicated to spectral measurements. I downloaded the book from

Chapter III has the title "Emission Spectra of Gases". The last paragraph in page 75 states:

"The hydrogen spectrum in the Schumann region, now under discussion, resembles the ordinary secondary spectrum in its complexity, but it is separated from it by a gap extending from $lambda=$2483 to $lambda=$1675; thus it appears to enjoy a separate existence. However, as the gap is filled by a continuous background apparently produced by hydrogen itself, the separation may be more apparent than real."

This was written about a century ago. Since Lyman was a gifted and careful experimentalist it can be assumed that there were solid facts behind his "continuous background apparently produced by hydrogen itself". My question aims to clarify if there is any contemporary experimental support for the existence of the continuous background he mentioned. Such continuous spectrum does not seem to conform the currently accepted quantum mechanical theory.

Let $H$ be the standard Schrödinger Hamiltonian operator for the hydrogen atom having stationary energy eigenvalues (as measured in eV)
E_0=-13.6, E_1=-13.6/4=3.4, E_2=-13.6/9=1.51 , ... , E_{n+1}=-13.6/n^2

On the basis of models and calculations to be discussed in future posts, the following conjectural statement can be made

CONJECTURE:
----------------
All hydrogen atom states $\psi$ with energy $E(\psi)$ satisfying
$$E_0 <E(\psi)<E_1$$
are energy stable.
----------------

In other words, these lower level stable states [LLSS] do not radiate spontaneously. In order for LLSS to radiate, they have to be "pumped" beyond energy $E_1$. LLSS states are trapped in an energy well. As a consequence Lyman series should not consists of lines but rather of bands. The bandwidth should be measured relative to the $E_1 - E_0$ energy gap.

Of course current quantum theory says that no such bands occur, but after reading Lyman's comment I decided to check against contemporary experimental results. Thus the request for actual spectrum plates and possible remarks by anyone familiar with the subject.

Most cordially,
Daniel Crespin
• Daniel Crespin · Central University of Venezuela
After a more detailed analysis of the non-linear space of states and evolution equation ---in the deterministic theory of atoms, called Realism--- it seems that the only stable stationary is the fundamental state. For the deterministic hydrogen atom no other states are stable. Excited stationary states are always unstable.

There remains the question of what explanation can be given ---or has already been given--- by spectroscopy for the "continuous background apparently produced by hydrogen itself " mentioned by Lyman in page 75 of his book, available at